On the other hand, one frequently finds in nuclear physics powerful deformed-mean-field calculations incorporating pairing, such as
Bardeen-Cooper-Schrieffer (BCS) [1]}, [2]}, [3]}, [4]} and Hartree-Fock-Bogoliubov (HFB) [5]}, [6]} calculations, which can be understood through Nilsson single-particle orbits [6]}, [8]}.
Calculations using deformed BCS and HFB have had great success in nuclear physics, but they break both rotational symmetry and particle number.
The BCS or HFB vacua are actually superpositions of states with different angular momentum quantum numbers in neighboring
(different particle number) nuclei.
One can restore the symmetries, for example recovering exact particle number by numerical integration over the gauge angle [6]}, [10]}, or good angular momentum by integration over Euler angles, where, for example,
the configuration space is constructed by angular momentum projection on quasiparticle states after solving the BCS/HFB equation in the Nilsson orbits [11]}, [12]}, [13]}.
